Question

question 8 1 pts a rectangular carton is designed to have a volume of 1.520 cubic meters. the carton is 1.18 meters high and 1.46 meters long. compute the width of the carton. 1.2881 m 1.2881 sq m 0.88 sq m 0.88 m

Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume \( V \) of a rectangular prism (carton) is given by \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height. We need to solve for \( w \), so we rearrange the formula to \( w=\frac{V}{l\times h} \).

Step2: Substitute the given values

We know \( V = 1.520 \, \text{m}^3 \), \( l = 1.46 \, \text{m} \), and \( h = 1.18 \, \text{m} \). First, calculate the product of length and height: \( l\times h=1.46\times1.18 \). Let's compute that: \( 1.46\times1.18 = 1.7228 \).

Step3: Calculate the width

Now, divide the volume by the product of length and height: \( w=\frac{1.520}{1.7228} \approx 0.88 \, \text{m} \). Wait, let's check the calculation again. Wait, maybe I made a mistake. Wait, \( 1.520\div(1.46\times1.18) \). Let's compute \( 1.46\times1.18 \): \( 1.46\times1.18 = (1 + 0.46)\times(1 + 0.18)=1\times1 + 1\times0.18+0.46\times1 + 0.46\times0.18 = 1 + 0.18 + 0.46 + 0.0828 = 1.7228 \). Then \( 1.520\div1.7228 \approx 0.88 \). Wait, but let's check the options. Wait, maybe I miscalculated. Wait, no, let's do the division properly. \( 1.520\div1.7228 \approx 0.88 \). Wait, but let's check the options. The options are 1.2881 m, 1.2881 sq m, 0.88 sq m, 0.88 m. Since width is a length, the unit should be meters, not square meters. So we can eliminate the options with sq m. Now, let's recalculate: Wait, maybe I messed up the formula. Wait, volume is length × width × height. So width = volume / (length × height). So \( w = 1.520 / (1.46 × 1.18) \). Let's compute 1.46 × 1.18: 1.461.18. Let's do 1.461 = 1.46, 1.46*0.18 = 0.2628, so total 1.46 + 0.2628 = 1.7228. Then 1.520 / 1.7228 ≈ 0.88. So the width is approximately 0.88 meters. Wait, but let's check the options. The last option is 0.88 m. So that's the correct one. Wait, but let's verify again. Wait, maybe I made a mistake in the formula. No, the formula for volume of a rectangular prism is correct. So length × width × height = volume. So width = volume / (length × height). So substituting the values: 1.520 / (1.46 × 1.18) = 1.520 / 1.7228 ≈ 0.88. So the correct option is 0.88 m.

Answer:

0.88 m (the option with "0.88 m")